Over a week ago, my rank, score and number of games played stat have frozen. Before, score would fluctuate constantly depending on my results, now nothing changes - even number of games played is stuck on 74.

Any ideas?

Should I re-install the app? I presume I could log back in after reinstallation and my purchases would still be intact?

As far as I know, your rank and score only ever change when you are playing Ranked games. I believe there is also a rank and score for solo games, but unranked games against other people doesn't do anything for either of you (except give you a chance to practice).